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We propose and demonstrate a method for improving optical-frequency sweepers that uses a disk-shaped optical bandpass filter operated under the synchro-scan mode. We optimize the filter layer structure to achieve high linearity in optical-frequency tuning with the rotation angle of the disk, while maintaining a constant band-inhibition performance. We introduce an optical system that narrows the bandwidth by using an optimized beam coupler and improves the filtering performance by using a multiple-path method. The optimized filter enables a stable linear optical-frequency sweep when it is used with a motor stabilized by phase locking. The improved optical frequency sweepers can extend the sweep range to above 2 THz, while suppressing the accumulation of spontaneous emission noise.